Static Electricity
In the preceding chapters, we concerned ourselves exclusively with electric
current i.e. electric- ity in motion. Now, we will discuss the behaviour of static electricity and the
laws governing it. In fact, electrostatics is that branch
of science which
deals with the phenomena associated with electric- ity
at rest.
It has been already
discussed that generally an atom is electrically neutral
i.e. in a normal
atom the aggregate of positive charge
of protons is exactly equal to the aggregate of negative charge
of the electrons.
If, somehow, some electrons
are removed from the atoms of a body, then it is left with a preponderance of positive charge.
It is then said to be positively-charged. If, on the other hand,
some electrons are added to it, negative charge
out-balances the positive
charge and the body is said to be
negatively charged.
In brief, we can say that positive electrification of a body results from
a deficiency of the electrons whereas negative electrification results
from an excess of electrons.
The total deficiency or excess of electrons in a body is
known as its charge.
Absolute and Relative Permittivity of a Medium
While discussing
electrostatic phenomenon, a certain property of the medium called its permittivity plays
an important role. Every medium is supposed to possess two permittivities :
(i) absolute permittivity (e) and (ii) relative permittivity (er).
For measuring relative permittivity, vacuum or free space is chosen as the reference medium. It has an
absolute permittivity of 8.854 ´ 10-12 F/m
Absolute permittivity e0 = 8.854 ´
10- F/m
12
Relative permittivity, er = 1
Being a ratio of two similar quantities, er has no units.
Now, take any other medium. If its relative permittivity, as
compared to vacuum is er, then
its absolute permittivity is e =
e0 er F/m
If, for example, relative permittivity of mica is 5,
then, its absolute permittivity is
|
e = e e = 8.854 ´ 10-12 ´ 5 =
44.27 ´ 10-12 F/m
Laws of Electrostatics
First Law. Like
charges of electricity repel each other, whereas unlike charges attract each
other.
Second Law. According to this law, the force exerted between
two point charges (i) is directly proportional to the product
of their strengths (ii) is inversely proportional to the square of the distance between them.
* Coulomb is better known for his law which states
that the force between two point charges is propor-
tional to each charge and inversely
proportional to the square of the distance between them.
4.1.
Electric Field
The region in which the stress
exists or in which electric
forces act, is called an electric field
or electrostatic field.
The stress is represented by
imaginary lines of forces. The direction of the lines of force at any point is the direction
along which a unit positive
charge placed at that point would move if free to do so.
It was suggested by Faraday
that the electric
field should be imagined to be divided
into tubes of force containing a fixed number of lines
of force. He assumed these tubes to
the elastic and having the property of contracting longitudinally the repelling laterally. With the help of these properties, it becomes easy to explain (i) why unlike charges attract
each other and try to come nearer
to each other and (ii) why like charges repel each other [Fig. 4.4 (a)].
However, it is more common to use the term lines
of force. These lines are supposed to emanate
from a positive charge and end on a negative
charge [Fig. 4.4 (b)]. These lines always leave or enter a conducting surface normally.
4.1.
Electrostatic Induction
It is found that when an uncharged body is brought
near a charged body, it acquires
some charge. This phenomenon of an uncharged body getting charged
merely by the nearness of a charged
body is known as induction. In Fig. 4.5, a positively-charged body A is brought
close to a perfectly-insulated
uncharged body B.
It is found that the end of B nearer
to A gets negatively charged whereas
further end becomes positively charged. The negative and positive charges of B are known as induced charges.
The negative charge of B is called
‘bound’ charge because it must remain on B
so long as positive charge of A remains there.
However, the positive
charge on the farther end of B is
called free charge. In Fig. 4.6, the body B has been earthed by a wire.
The positive charge
flows to earth leaving
negative charge behind.
If next A is removed, then this negative
charge will also go to earth, leaving B uncharged. It is found that :
(i) a positive charge induces a negative charge and vice-versa. each of the induced charges is equal to the inducing charge.
(ii)
4.1.
Electric Potential
and Energy
We know that a body raised above
the ground level
has a certain amount of mechanical potential energy which, by definition, is
given by the amount of work done in raising it to that height. If, for example, a body of 5 kg is raised against gravity
through 10m, then the potential energy
of the body is 5 ´ 10 = 50 m-kg. wt. = 50 ´
9.8 = 490 joules. The body falls because there is attraction due to gravity
and always proceeds
from a place of higher potential
energy to one of lower potential energy. So, we
speak of gravitational potential energy or briefly ‘poten- tial’ at different points in the earth’s gravitational field.
Now, consider an electric field. Imagine an isolated positive charge Q placed in air (Fig. 4.15). Like earth’s gravitational field, it has its own electrostatic field which theoretically extends upto infinity. If the charge X is very far away from Q, say, at infinity, then force on it is practically zero. As X is brought nearer to Q, a force ofrepulsion acts on it (as similar charges repel each other),
Fig. 4.15 hence work or energy is required to bring it to a point like A in the electric field. Hence, when at point A, charge X has some amount of electric potential energy. Similar other points in the field will also have some potential energy. In the gravitational field, usually ‘sea level’ is chosen as the place of ‘zero’ potential. In electric field infinity is chosen as the theoretical place of ‘zero’ potential although, in practice, earth is chosen as ‘zero’ potential, because earth is such a large conductor that its potential remains practically constant although it keeps on losing and gaining electric charge every day.
4.2.
Potential and
Potential Difference
As explained above, the force acting
on a charge at infinity
is zero, hence ‘infinity’ is chosen as the theoretical place of zero electric
potential. Therefore, potential at any point in an electric field may be
defined as
numerically equal to the work done in bringing
a positive charge of one coulomb from infin-
ity to that point against the electric field.
The unit of this potential will depend on the unit of
charge taken and the work done.
If, in shifting one coulomb from infinity to a certain
point in the electric field,
the work done is
one joule, then potential of that ponit is one
volt.
Obviously, potential is work per unit charge,
Similarly, potential difference (p.d.) of one volt exists between
two points if one joule of work is
done in shifting a charge
of one coulomb from one point to the other.
4.1.
Breakdown Voltage and Dielectric Strength
An insulator or dielectric is a substance within which there
are no mobile electrons necessary for electric conduction. However,
when the voltage
applied to such an insulator exceeds a certain
value, then it breaks
down and allows
a heavy electric
current (much larger
than the usual
leakage current) to flow
through it. If the insulator is a solid medium, it gets punctured or cracked.
The disruptive or breakdown voltage of an insulator is the minimum
voltage required to break it down.*
Dielectric strength of an insulator or
dielectric medium is given by the maximum potential difference which a
unit thickness of the medium can withstand without breaking down.
In other words, the dielectric strength
is given by the potential gradient necessary to cause break- down of an insulator. Its unit is
volt/metre (V/m) although it is usually expressed in kV/mm.
For example, when we say
that the dielectric strength of air is 3 kV/mm, then it means that the maximum p.d. which one mm thickness
of air can withstand across it without
breaking down is 3 kV or 3000 volts. If the p.d. exceeds this
value, then air insulation breaks down allowing large electric current to pass through.
Dielectric strength
of various insulating materials is very important factor in the design of high-
voltage generators, motors and transformers. Its value depends on the thickness
of the insulator, temperature, moisture, content, shape and several other factors.
For example doubling the thickness of insulation does not double
the safe working
voltage in a machine.**
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* Flashover is the disruptive discharge which taken places over the surface
of an insulator and occurs
when the air surrounding it breaks down. Disruptive conduction is luminous.
** The
relation between the breakdown voltage V and
the thickness of the dielectric is given approximately by the relation V = At2/3
where
A is a constant depending on the
nature of the medium and also on the thickness t. The above statement is known as Baur’s law.
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Table No. 4.1 Dielectric Constant and Strength (*indicates
average value) |
||
|
Insulating
material |
Dielectric constant or relative permittivity (er) |
Dielectric Strength in kV/mm |
|
Air |
1.0006 |
3.2 |
|
Asbestos* |
2 |
2 |
|
Bakelite |
5 |
15 |
|
Epoxy |
3.3 |
20 |
|
Glass |
5-12 |
12-100 |
|
Marble* |
7 |
2 |
|
Mica |
4-8 |
20-200 |
|
Micanite |
4-5-6 |
25-35 |
|
Mineral Oil |
2.2 |
10 |
|
Mylar |
3 |
400 |
|
Nylon |
4.1 |
16 |
|
Paper |
1.8-2.6 |
18 |
|
Paraffin wax |
1.7-2.3 |
30 |
|
Polyethylene |
2.3 |
40 |
|
Polyurethane |
3.6 |
35 |
|
Porcelain |
5-6.7 |
15 |
|
PVC |
3.7 |
50 |
|
Quartz |
4.5-4.7 |
8 |
|
Rubber |
2.5-4 |
12-20 |
|
Teflon |
2 |
20 |
|
Vacuum |
1 |
infinity |
|
Wood |
2.5-7 |
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